Orthonormal Basis, Bra–Ket Notation, and Measurement

In this chapter, we emphasize the importance of orthonormal bases and normalized vectors in quantum computing. They make the math simple, and they are necessary in order to make a quantum state physically meaningful. Particularly, we find that this is also closely related to the measurement of a quantum state, in which the probability of a normalized quantum state collapsing to a certain basis state is equal to the square of the magnitude of the corresponding coefficient. We will also improve our skills in using the bra–ket notation.